/* mpi-inv.c  -  MPI functions */

#include "mpi-internal.h"

/****************
 * Calculate the multiplicative inverse X of A mod N
 * That is: Find the solution x for
 *		1 = (a*x) mod n
 */
int mpi_invm(MPI x, MPI a, MPI n)
{
    /* Extended Euclid's algorithm (See TAOCP Vol II, 4.5.2,
     * Alg X) modified according to Michael Penk's solution
     * for Exercise 35 with further enhancement
     */
    MPI          u, v, u1, u2 = NULL, u3, v1, v2 = NULL, v3, t1, t2 = NULL, t3;
    unsigned int k;
    int          sign;
    int          odd;

    if (!mpi_cmp_ui(a, 0)) return 0; /* Inverse does not exists.  */
    if (!mpi_cmp_ui(n, 1)) return 0; /* Inverse does not exists.  */

    u = mpi_copy(a);
    v = mpi_copy(n);

    for (k = 0; !mpi_test_bit(u, 0) && !mpi_test_bit(v, 0); k++) {
        mpi_rshift(u, u, 1);
        mpi_rshift(v, v, 1);
    }
    odd = mpi_test_bit(v, 0);

    u1 = mpi_alloc_set_ui(1);
    if (!odd) u2 = mpi_alloc_set_ui(0);
    u3 = mpi_copy(u);
    v1 = mpi_copy(v);
    if (!odd) {
        v2 = mpi_alloc(mpi_get_nlimbs(u));
        mpi_sub(v2, u1, u); /* U is used as const 1 */
    }
    v3 = mpi_copy(v);
    if (mpi_test_bit(u, 0)) { /* u is odd */
        t1 = mpi_alloc_set_ui(0);
        if (!odd) {
            t2       = mpi_alloc_set_ui(1);
            t2->sign = 1;
        }
        t3       = mpi_copy(v);
        t3->sign = !t3->sign;
        goto Y4;
    } else {
        t1 = mpi_alloc_set_ui(1);
        if (!odd) t2 = mpi_alloc_set_ui(0);
        t3 = mpi_copy(u);
    }

    do {
        do {
            if (!odd) {
                if (mpi_test_bit(t1, 0) || mpi_test_bit(t2, 0)) {
                    /* one is odd */
                    mpi_add(t1, t1, v);
                    mpi_sub(t2, t2, u);
                }
                mpi_rshift(t1, t1, 1);
                mpi_rshift(t2, t2, 1);
                mpi_rshift(t3, t3, 1);
            } else {
                if (mpi_test_bit(t1, 0)) mpi_add(t1, t1, v);
                mpi_rshift(t1, t1, 1);
                mpi_rshift(t3, t3, 1);
            }
        Y4:;
        } while (!mpi_test_bit(t3, 0)); /* while t3 is even */

        if (!t3->sign) {
            mpi_set(u1, t1);
            if (!odd) mpi_set(u2, t2);
            mpi_set(u3, t3);
        } else {
            mpi_sub(v1, v, t1);
            sign    = u->sign;
            u->sign = !u->sign;
            if (!odd) mpi_sub(v2, u, t2);
            u->sign  = sign;
            sign     = t3->sign;
            t3->sign = !t3->sign;
            mpi_set(v3, t3);
            t3->sign = sign;
        }
        mpi_sub(t1, u1, v1);
        if (!odd) mpi_sub(t2, u2, v2);
        mpi_sub(t3, u3, v3);
        if (t1->sign) {
            mpi_add(t1, t1, v);
            if (!odd) mpi_sub(t2, t2, u);
        }
    } while (mpi_cmp_ui(t3, 0)); /* while t3 != 0 */
    /* mpi_lshift( u3, k ); */
    mpi_set(x, u1);

    mpi_free(u1);
    mpi_free(v1);
    mpi_free(t1);
    if (!odd) {
        mpi_free(u2);
        mpi_free(v2);
        mpi_free(t2);
    }
    mpi_free(u3);
    mpi_free(v3);
    mpi_free(t3);

    mpi_free(u);
    mpi_free(v);
    return 1;
}
